With a small tweak in assumptions and the inexorable force of compound
arithmetic, Citigroup and HSBC have come up with radically different
pictures of what the world will look like in 2050.

Which of the two is closer to the mark will determine whether the West hangs on, or disappears as a relevant voice in global affairs.

For neo-Spenglerites - who believe the West is finished - Citigroup’s Willem Buiter offers some astonishing projections. The Muslim powerhouse of Indonesia will alone match the combined GDP of Germany, France, Italy, and Britain by mid-century.

The economies of China and India will together be four times as large as the United States, restoring the historic order of Asian dominance before Europe’s navies burst on the scene in the 16th Century. Panta Rei, says Dr Buiter: all is in flux; nothing will remain the same.

Africa will at last emerge from its long string of disappointments to take the baton as the fastest growing region, clocking 7.5pc a year over the next two decades.

It does not require miracles of performance for this to occur. Catch-up countries merely need to keep reforms on track, open markets, “don’t be unlucky, and don’t blow it”, and let convergence theory do the work for them.

Having rid themselves of calamitous nonsense – Maoism, the Hindu model, and other variants of central planning or autarky – and having at last achieved a “threshold level” of law and governance, nothing should stop them, or so goes the argument.

“Sustained growth prospects in per capita incomes across the world have not been as favourable as they are today for a long time, possibly in human history.” Global growth will quicken. GDP will quadruple again from $73 trillion to $378 trillion by 2050 (constant US dollars).

Dr Buiter’s team adds the usual caveats: “beware of compound growth rate delusions;” or “the bigger the booms, the more spectacular the bubbles, and the devastating the busts;” or indeed that “convergence is neither automatic, nor inevitable. In history, it has been more the exception than the rule.”

Argentina is a salutary lesson. Why did it diverge from its sister economy Australia, so similar in trading patterns in the late 19th Century? Why did it fall from the world’s fifth richest in per capita terms in 1900 to a third of Australia’s level a century later?

It is hard to pin-point where the rot began, though Peron clinched decline by bleeding farm wealth to fund his populist patronage, and by forcing the central bank to print the shortfall. Bad policies hurt.

Oddly, Britain will scrape through in Citigroup’s global reshuffle, just holding on as the world’s 10th biggest economy in 2050, the only EU state left in the top ten. It will even overtake the US in per capita terms.

Can this be so? Britain has slipped to 25th in reading, 28th in maths, and 16th in science in the Pisa rankings. Shanghai’s school district takes top prize across all three, ahead of Korea and Finland. While the UK faces a less disastrous ageing crisis than much of Europe, this is thanks to our unrivalled leadership in unwed teenage pregnancies.

HSBC’s report also sketches an era of unparalleled prosperity, yet the West does not sink into oblivion. China overtakes the US, but only just, and then loses momentum.

Chimerica, not Chindia, form the G2, towering over all others in global condominium. Americans prosper with a fertility rate of 2.1, high enough to shield them from the sort of demographic collapse closing in on Asia and Europe. Beijing and Shanghai are 1.0, Korea is 1.1, Singapore 1.2, Germany 1.3, Poland 1.3, Italy 1.4 and Russia 1.4.

Americans remain three times richer than the Chinese in 2050. The US economy still outstrips India by two-and-a-half times. This is an entirely different geo-strategic outcome.

My own view is closer to HSBC, perhaps because my anthropological side gives greater weight to the enduring hold of cultural habits, beliefs, and kinship structures, and because of an unwillingness to accept that top-down regimes make good decisions in the end.

Both studies rely on the theories of Harvard economist Robert Barro, but differ on how easy it is to handle population collapse. The great unknown is what rapid ageing does to creative zest, and how many decades it takes to turn the demographic super tanker.

China’s workforce peaks in absolute terms in four years. While the population keeps growing until the tipping point in the mid 2020s, it is ageing very fast. Hence warnings by Chinese demographers that there may soon be an epidemic of suicides, as the elderly step out on the ice to relieve the burden.

Zhuoyan Mao from Beijing’s Institute for Family Planning said China’s fertility rate had been below replacement level for almost twenty years. “Population momentum” turned negative over a decade ago in Beijing, Tianjin, Shanghai and Liaoning, but the countryside is catching up. “The decline speed in rural areas is faster,” he says.

It is bizarre that China should still cling to the one-child policy, though Shanghai’s local authorities have been encouraging couples to have a second child since 2009. The policy is losing its relevance at this stage, though gender picking (female infanticide, at the ultrasound stage) has left the legacy of a male/female ratio of 1.2 to 1, with all that implies for social stability.

China’s fertility rate is collapsing anyway for the same reasons as it has collapsed in Japan and Korea – affluence, women’s education, later pregnancies that stretch generations, in-law duties, and costly housing. You cannot reverse this with a wave of the wand. The lag times can be half a century.

George Magnus, UBS’s global guru, writes in his book “Uprising” that China faces a “triple whammy of ageing”. The number of children under 14 will fall by 53m by 2050; the work force will contract by 100m; and the over-60s will rise by 234m, from 12pc to 31pc of the total.

Mr Magnus is scathing about the “muddled thinking” of those who fall for BRICs hysteria, or who succumb to the facile conclusion that the global credit crisis finished the West and served as catalyst for a permanent hand-over to Asia.

The crisis also exposed the fragility of Asian mercantilism, even if this has been disguised for now by a stimulus blitz in China that has pushed credit to 200pc of GDP.

I might add that China is depleting the non-renewable aquifers of its northern plains at an alarming place, and faces a separate water crisis from receding Himalayan glaciers.

Cheng Siwei, the head of China’s green energy drive, told me a few months ago that eco-damage of 13.5pc of GDP each year outstrips China’s growth rate of 10pc. "We have an intangible environmental debt that we are leaving to our children," he said. That debt is already due.

Perhaps the 21st Century will be America’s after all, just like the last.